Abstract This paper is about the compositional interpretation of adverbial clauses as introduced by insofern als (lit. ‘insofar as’) in German (= IAs); for example, Die Lösung ist insofern attraktiv, als sie günstig ist. (lit. ‘The solution is insofar attractive as it is cheap.’). I argue that IAs always contribute dimensional restrictions, but do so in two distinct structure-sensitive ways: IAs can be structurally integrated into their host clauses and, thus, dimensionally specify a lexical component of the matrix VP (= LIAs) (‘The solution is attractive in price.’); alternatively, they can be structurally non-integrated and, thus, provide a dimension against which the matrix sentence is evaluated holistically (= SIAs) (‘In light of the fact that the solution is cheap, one may say that it is attractive.’). The proposal is supported by both syntactic and semantic-pragmatic evidence: (i) LIAs and SIAs are distinguished by independently motivated tests for structural (non)integration such as scope of negation and particles, focus-background structure, and variable binding. (ii) LIAs are sensitive to a lexically given multidimensional matrix predication. SIAs, by contrast, require that the embedded clause specify an objective justification for the truth of the matrix proposition as a whole. In particular, IAs are shown to not pass tests for subjectivity as discussed for finden (‘find’); for example, judge- dependency, resistance against denial, or, accessibility of a subjective attitude. The paper concludes by sketching a formal derivation of both readings. Accordingly, LIAs constrain the dimensional parameter of multidimensional lexical predications, while SIAs provide facts that de re justify the assertibility of predications for topic situations.